An appeal from a 56-year-old British grandmother on Texas death row is being sent back to her trial court in Houston for additional review.

Lawyers for 56-year-old Linda Carty contend prosecutors coerced witnesses into giving false evidence at the trial where she was convicted and condemned for the 2001 murder of her neighbour, Joana Rodriguez, and the abduction of Rodriguez's four-day-old son.

Their appeal to the Texas Court of Criminal Appeals also argues prosecutors arranged for a deal with a co-defendant that wasn't disclosed to defence lawyers and that four jurors now say they either would have acquitted Carty or not given her a death sentence.

The Harris County prosecutor's office said on Wednesday it is investigating the claims.

Carty, from the British Virgin Islands, had lived in Houston for nearly 20 years.